Question

Prove that sin^2 75° - sin^2 15° = √3/2​

Answer 1

Answer:

Value\: of \:sin^{2}75-sin^{2}15=\frac{3}{4}

Step-by-step explanation:

Given sin²75°- sin²15°

= sin²(90°-15°)-sin²15°

= cos²15°-sin²15°

/* sin(90-x) = cosx */

= cos (2×15°)

/* cos²x-sin²x = cos2x */

= cos² 30°

= \left(\frac{\sqrt{3}}{2}\right)^{2}

= \frac{3}{4}

Therefore,

Value\: of \:sin^{2}75-sin^{2}15=\frac{3}{4}